Problem: Solve for $x$ and $y$ using elimination. ${-2x+6y = 48}$ ${-5x+5y = 20}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-2$ ${-10x+30y = 240}$ $10x-10y = -40$ Add the top and bottom equations together. $20y = 200$ $\dfrac{20y}{{20}} = \dfrac{200}{{20}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-2x+6y = 48}\thinspace$ to find $x$ ${-2x + 6}{(10)}{= 48}$ $-2x+60 = 48$ $-2x+60{-60} = 48{-60}$ $-2x = -12$ $\dfrac{-2x}{{-2}} = \dfrac{-12}{{-2}}$ ${x = 6}$ You can also plug ${y = 10}$ into $\thinspace {-5x+5y = 20}\thinspace$ and get the same answer for $x$ : ${-5x + 5}{(10)}{= 20}$ ${x = 6}$